descartes s rules for the direction of the mind 1957

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OSMANIA UNIVERSITY LIBRARYCall No. \RM ' 1 Accession No. U O t> OX t2.I>Author -x-oO'i.V'v'NA , \\CXx


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DESCARTES'S RULES FOR THEDIRECTION OF THE MIND


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DESCARTES'S RULESFOR THE

DIRECTION OF THE MIND

by the lateHAROLD H. JOACHIMFormerly Wykeham Professor of Logic

In the University of Oxford

Reconstructed from Notestaken by his Pupils

Edited by Errol E. HarrisForeword by Sir David Ross

LondonGEORGE ALLEN & UNWJN LTD


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FIRST PUBLISHED IN 1957This book is copyright under the Berne Convention.Apart from any fair dealing for the purposes ofprivate study, research, criticism or review, as per-mitted under the Copyright Act 1911, no portion maybe reproduced by any process without written per-mission. Enquiry should be made to the publisher.

PRINTED IN GREAT BRITAINin n 1 12 pt. Pilgrim type

BY EAST MIDLAND PRINTING COMPANY LTD,BURY ST. EDMUNDS AND ELSEWHERE


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EDITOR'S PREFACE

During the early 1930*5, Harold H. Joachim, as WykehamProfessor of Logic at Oxford, delivered the Logical Studiesas a course of lectures extending over two terms of theacademic year, and in the third term he delivered a setof lectures on the Regulae of Descartes. The Logical Studies,have long since been published, but the manuscript of theDescartes lectures was lost, and there is reason to believethat it was accidentally destroyed with certain domesticpapers of no philosophical importance. With the extinctionof all hope of finding the original manuscript it seemsfitting that, rather than submit to the complete loss of thiswork to the world of scholarship, an attempt should bemade to reconstruct it from the notes taken by some ofthose who heard the lectures. Two sets of notes (all, sofar as I can ascertain, that are available) have been usedfor this purpose: those of Mr. John Austin, now White'sProfessor of Moral Philosophy at Oxford, and my own.Let me at once record my gratitude to Professor Austinfor the use he has allowed me of his excellent set of notes.It was my own endeavour as a student to get down, so faras was physically possible, every word of Joachim'slectures, but Professor Austin, by adopting a more tele-graphic style, succeeded in recording even more of thesubstance and detail of the lectures than I had.

In attempting to reconstruct what Joachim had actuallywritten, I have tried not to omit anything of the least


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importance which is contained in either set of notes.Where they were verbally identical little difficulty pre-sented itself and it seemed safe to presume that here onehad very nearly, if not exactly, what the lecturer hadsaid. Where the notes differed verbally but not in sense,I have adopted, whichever rendering seemed to me to ex-press better the thought of the author as I remember it.If in this respect there was little to choose between thetwo versions, I have adopted the one which (with leastadjustment or modification) would read better. But bothversions are no more than students' notes, taken in lecturesand written under pressure of time, and it has been neces-sary throughout to make minor corrections and to supplyomissions, both in order to produce a continuous prosestyle and in order to clarify the meaning. That these cor-rections and intercalations are even near to what Joachimwrote or would have written (had he lived to revise thework) there is, of course, no means of knowing, but Ihave constantly kept in mind the sort of thing that Iremember he used to say as well as what he has writtenelsewhere.

If Joachim had lived it is almost certain that he wouldnot have permitted the publication of his own notes beforehe had carefully revised them more than once. He wouldprobably have corrected and modified them or even re-written them either wholly or in part. He would pre-sumably have written a conclusion to avoid the abrupt-ness with which these lectures end. In short, the publica-tion of the present version is to be tolerated only as alesser evil than the total loss of the thought and work onthis subject of one of the most erudite and carefulscholars of the last generation.

It is, further, regrettable that the appearance of thiswork of Joachim's should have been so long delayed. Butit was necessary to make sure that no original, nor anybetter and more authentic version, was ever likely to be-


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come available before resorting to the very inferior sub-stitute of students' notes. In the meantime further researchhas been done on the subject of Descartes's method and,in particular on the Regulce. New editions (e.g. by Leroyand Gouhier) have appeared and a number of works inFrench, besides Dr. L. J. Beck's admirable book in English.The reader will have to bear in mind that Joachim'slectures predate all these, and that much which he wrotein 1930 (or thereabouts) he would undoubtedly have re-considered had he lived to read and know of this morerecent work. But the extent to which he would have modi-fied his own writing cannot be known. I have, therefore,made no attempt to edit the lectures in the light of laterresearch. It is not impossible that scholars writing afterJoachim would themselves have been influenced by histhought had it been published in time. It seems to me that,in the circumstances, it is important to make this littlework available in the best form possible without moreado, as something of lasting value to philosophers ingeneral and to Cartesian scholars in particular. It is notfor me (or, as I see it, for even more competent persons)to correct what Joachim wrote in the light of laterscholarship as it cannot be known whether, to what ex-tent, or in what way, he would have done so himself.

There is one further consideration. The contemporaryidiom in Anglo-Saxon philosophy is so utterly differentfrom that in which Joachim wrote and thought onlytwenty years ago, that many students may question thevalue of this publication. That the work is at least ofhistorical interest, both in itself and as a contribution tothe history of philosophy no genuine scholar will deny.But it is of even greater value than that in as much as itis a contribution (far greater than its physical size sug-gests) to a kind of philosophy which, if it is at presentnot so widely practised, nevertheless, has in it much soundsubstance and significance, and one which may well re-


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turn to fashion in the not far distant future. There aresigns that, for all their vigour, contemporary empiricismshave reached the limit of profitable development. Evenprofessional philosophers may shortly be forced to lookelsewhere for fruitful means of advance, if only by thepressure exerted upon them by the progress of the naturalsciences, the direction of which seems to point to aphilosophy very different from that now current, or bythe demand for a re-interpretation of human experience,which the inescapable course of international politicsmakes upon them.

It remains only for me gratefully to acknowledge theassistance of the University of the Witwatersrand whosesubvention has made the publication of this book possible.ERROL E. HARRIS

The University of the WitwatersrandJohannesburg


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CONTENTS

EDITOR'S PREFACE5

INTRODUCTIONpage 13

I THE POWER OF KNOWINGpage 19

II THE CARTESIAN METHODpage 62

III PHILOSOPHICAL ANALYSISOF THE CONCRETEpage 100

INDEX


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FOREWORD

I have gladly accepted Professor Harris's invitation to meto write a brief introduction to his edition of ProfessorJoachim's lectures on Descartes's Rules for the Directionof the Mind. I had the good fortune of knowing ProfessorJoachim for the last forty years of his life. His philosophi-cal views have been admirably described and discussed inJoseph's memoir of him in vol. 24 of the Proceedings ofthe British Academy, and any who wish to see a sym-pathetic and yet critical account of them cannot do betterthan read that memoir. My own attitude towardsJoachim's philosophy is not unlike that of Mr. Joseph. Icannot accept Joachim's coherent theory of truth. But Igreatly admire its scholarship and exactness of his ex-position, whether the philosopher he was concentrating onwas Aristotle or Descartes or Spinoza; in each of thosefields of study, he was a master. In the interpretation ofAristotle the student's first task is to discover whatAristotle actually wrote, and that involves the carefulstudy of the manuscript tradition and of the ancient com-mentators, and the establishment of a correct text, inwhich even the punctuation is a matter of importance.Joachim's scholarship and skill in all this I was able toobserve at the weekly meetings of the Oxford AristotilianSociety from 1900-1914, and in reading his recentlypublished commentary on the Nicomachean Ethics.His work on Descartes and on Spinoza exhibits the samequalities of scholarship and of philosophical acumen. Hisbook on Spinoza is the best study in the English language


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at any rate of this great philosopher. Professor Harris hasbeen able to reconstruct, from his own notes and thoseof other pupils, Joachim's lectures on Descartes, theoriginal manuscript of which was unfortunately lost. Inthis reconstruction some of the nuances of his expositionwill no doubt have been lost, but enough remains to makeProfessor Harris's edition a most valuable contribution tothe study of Descartes.Mr. T. S. Eliot, who was Joachim's pupil at MertonCollege, has borne testimony to the close but luminousstyle (to quote the words of the present Warden ofMerton) of his writing; and any of his philosophicalcolleagues at Oxford who are still alive would bear testi-mony to the clarity and firmness (combined with exquisitecourtsey) with which he would expound his views orcriticise those of others. Professor Harris's book will revivein our minds the impression which Joachim made in ouroral discussions.

W. D. Ross.


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INTRODUCTION

Charles Adam suggests that the Regulae ad Direction-em Ingenii, the unfinished dialogue, La Recherche de laVerite par la Lumiere Naturelle, and Le Monde are re-lated to Discours de la Methode, Meditationes andPrincipia Philosophiae as the first crude sketch for afinished masterpiece. 1 This view is fully confirmed bycomparison of the Regulae with the Discours.The Discours was first published in 1637 (whenDescartes was 41 years old) as the exposition of thegeneral principles of the Cartesian method. It ismasterly in conception and exposition, as well as inits lucidity and coherence. The Regulae, in contrast,was written probably in the winter of 1628-9, or evenearlier, and is unfinished2 and in many ways imperfect.The work is immature and was probably left un-finished because of its defects. Descartes is still, in somerespects, feeling his way. His exposition is often con-fused and rambling and is sometimes inconsistent. Heis more dogmatic than in the later works, in whichsome of the doctrines here stated are rejected ormodified. The work is also immature in form. For1 Cp. Adam & Tannery, X, pp. 530-2 and XII, pp. i46ff.2 There were to have been 36 rules (cf. Reg. xii), but only 23 exist,and the last three lack explanatory expositions.

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example, Rule xi 1 merely repeats Rule vi2 in a com-pressed form; the long autobiographical passage at theend of the exposition of Rule iv3 seems to have beenadded as an afterthought and is ill-fitting in that place,and Rule viii combines, without reconciliation, a roughdraft with a more finished but incompatible version.Owing to these defects, most editors pass over the

Regulae with brief notice, and the accepted and auth-oritative account of Descartes's method is based on theDiscours. But a detailed study of the Regulae is in-structive as well as interesting, if for no other reasonthan that it constitutes the first material for the exam-ination of the Cartesian conception of vera mathesis.Though nothing emerges in the Regulae which is ir-reconcilable with the traditional exposition of themethod, yet it presents difficulties which do not ap-pear

in the Discours, and so provides a fuller under-standing of Descartes's teaching.

HISTORY OF THE MSS4Descartes died at Stockholm on the nth February,

1650. Two inventories of his papers were made, oneat Stockholm, on the i4th of February, of papers hehad brought into Sweden, and the second at Leyden, onthe 4th of March, of papers left in Holland. M. Jean deRaey, a Professor at Leyden and friend of Descartes,testifies that these were few and of small importance1 A. and T., X, pp. 409-410.2 Ibid., pp. 384-7.3 Ibid., pp. 374-9-4 Cp. A. & T., X, pp. 1-14, 351-7, 486-8,

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as Descartes took the best with him to Sweden. 1 Ofthe earlier inventory, made 3 days after Descartes'sdeath, two manuscript copies survive.2 There are 23rubrics and the Regulae is mentioned under RubricF : 'Neuf cahiers reliez ensemble, contenans partie d'untraite des regies utiies et claires pour la direction de1'Esprit en la recherche de la Verite'.*

All (except domestic papers) that were contained inthis inventory were entrusted to M. Chanut, Frenchambassador to Queen Christina of Sweden; he convey-ed them to Paris, and, being too busy himself to pub-lish any of the manuscripts, entrusted all or most ofthem to his brother-in-law Clerselier4 who was also afriend of Descartes.

Clerselier published three volumes of letters in 1657,1659 and 1667. He also published, in one volume, atreatise on Man (L'homme), in 1664, and in thesecond edition (1677) added 'Le Monde (ou Traite de laLumiere). In a preface to Vol. Ill of the letters, Cler-selier says that there are still more than enough MSS.to make another volume of fragments and offers themto anyone who is willing to edit them. Nobody accep-ted the offer and Clerselier died in 1684 leaving themunpublished. He passed the MSS. on to the Abbe JeanBaptiste Legrand who set out admirably to produce acomplete edition of all Descartes's posthumous works,but he died in 1704 before the edition was finished,leaving its completion to Marmion. But he too died,1 A. & r, v, p. 410.2 A. & T., X, pp. s-12.3 Ibid. p. 9.4 Vide ibid., p. 13.


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in 1705. There does exist in Paris a richly annotatedcopy of Clerselier's three volumes with marginal notes,additions and corrections in the hand of Legrand,of Marmion and of Baillet (Descartes's biographer).After Marmion's death the papers reverted to Leg-rand's mother and it is not known what became ofthem thereafter. The MS. of the Regulae has thus van-ished, but a number of people saw and used it : (i) Thesecond edition of the Port Royal Logic (Arnaud andNicole, I664 1) contains a long extract from Rules xiiiand xiv translated into French. This the editors owedto Clerselier who lent them the MS.2 (ii) NicolasPoisson in his Remarques sur la Methode de M. Des-cartes (1670) says that he saw the MS.3 (iii) PerhapsClerselier also showed it to Malebranche, who himselfpublished a work in 1674-5 under the same title asLe Recherche de la Verite. (iv) Baillet, in his Life ofDescartes (1691) quotes the Regulae freely and usesthem in many places. He says Legrand lent him theMS.4 (v) A note discovered at Hanover in Leibniz'shandwriting says that with Tschirnhaus he visitedClerselier, who showed them both certain MSS of Des-cartes including Le Recherche de la Verite and '22 rulesexplained and illustrated'.

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At least two MS. copies of the Regulae were madein Holland. One was bought by Leibniz in September1670 from Dr. Schuller for the Royal Library at Han-over, where it now remains. It is an inferior version1 The first edn. appeared in 1662.2 Vide A. & T., X, p. 352.3 Ibid.4 Cp. ibid.5 Cp. ibid. pp. 208-9.

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with many omissions and mistakes. Leibniz (not at thetime knowing Descartes's handwriting) says that it isin the author's own hand, but this is not the case. Theother copy is much better and probably belonged toJean de Raey. It was used for the Flemish translationof 1684 by Glazemaker and served, no doubt, as theoriginal for the Amsterdam edition of OpusculaTostuma of 1701. The version given by Adam andTannery is based primarily on this, which they referto as 'A', correcting it at times from the Hanover MS.(for which the reference is H).

DATE OF COMPOSITION1Adam suggests the winter of 1628-9 as the timewhen Descartes wrote the Regulae. Between 1629 and

1650 Descartes's letters give much information abouthis writings but say nothing of the Regulae. He isknown to have spent the years 1618-25 travellingand soldiering; from 1625 to 1628 he stayed in Paris,which he found distracting and so unfavourable tostudy that he decided to go into retirement and, beforehe repaired to Holland 'to seek solitude'2 (as we learnfrom one of his letters), he spent the winter in thecountry in France 'where he made his apprenticeship/3It seems from the context, however, that this meanslittle more than that he accustomed himself to solitudeat this time. Adam, nevertheless, suggests that it wasthen that the Regulae was written; but Gilson believesthat it can be put much earlier and goes back to the1 Cp. A. & T., X. pp. 486-8.2 A. & T., X, p. 487.3 A. & T., V, p. 558.

B *7


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time when Descartes was engaged on his first work,which was to have been called, Studium Bonae Mentis.

THE ORIGINAL TITLEIn the A version the title given is 'Regulae ad Direc-

tionem Ingenii' : in the H. Version 'Regulae ad Inquir-endam Veritatem'. Baillet combines these and Leibnizrefers to The Search after Truth*. Perhaps the originalMS. had both, either as alternatives or combined asBaillet has them.


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CHAPTER ITHE POWER OF KNOWING

RULE i : The first of Descartes's rules is not quite assimple and obvious as it appears. The ultimate aim ofstudy should be to guide the mind so that it can passsolid and true judgements on all that comes before it.

In the exposition Descartes begins by contrasting artor craft with science or speculative knowledge. Art in-volves the acquisition of some special bodily skill, sono one person can be master of all the arts. Scienceneeds no bodily training, no development of the bodyor any part of it. The power of knowing is a purelyspiritual power, single, self-identical and absolute (asopposed to bodily skills). It retains its single characterin every field. One may call it 'human or universalwisdom', or 'good sense* (bona mens), or the 'nat-ural light' of reason. It must be regarded as a spirituallight which is no more modified by the diversity of theobjects it illuminates than is sunlight by the things onwhich it shines. It is an intellectual vision, a single,natural power of discriminating the true from thefalse.The knowledge of a science (unlike a craft) does

not destroy, but increases the power to learn others.19


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All sciences are interconnected, so that it is easier tolearn all together than each in isolation. They are sim-ply the universal wisdom variously applied. If we wantto search for the truth about things, therefore, wemust make it our object to increase the natural light ofreason in ourselves. The same vis cognoscens is atwork throughout, and we must make it our whole aimto increase this perfectly general power. Indeed thereare legitimate results to be had from the study of thespecial sciences (e.g. the cure of disease and the sup-reme pleasure of the vision of new truth); but thesespecial rewards are irrelevant and to aim primarily atthem would be to endanger the success of our mainenterprise. We must think only of cultivating the nat-ural light.The last sentence of the exposition of Rule i 1 seemsto insist on the supremacy of the practical end, butfull and careful study shows that Descartes's realpurpose was to demonstrate the identity of reasonin speculation and in practice. The same bona mensis the condition both for the discovery of truthand for the conduct of life. Intelligent insight mustprecede judgement. All judgement whether specula-tive or practical is for Descartes (or so at least he sayslater) an act of will assent to or dissent from an ideawhich soon goes beyond all knowledge by mereobservation. Thus it is better to pursue studies with ageneral aim than to work at special problems.We must attend to two matters in this exposition :(i) The severance of the power of knowing from allcorporeal functions and (ii) its singleness, (i) The first1 A. & T., X, p. 361.20


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is only lightly touched on here. In the exposition ofRule xii, 1 however, he supplements this and sketchesin detail his view of the knowing subject, the doctrineunderlying which seems to be the same as that elabor-ated in the Meditationes and the Prmcipia Thiloso-phiae (I, viii, et. seq). In Rule xii, however, he doesnot attempt to explain what the mind or the body is orhow the body is informed by mind, but is content toput forward his theory of the knowing subject merelyas an hypothesis, which may be summarized as fol-lows :There are in the knowing subject four faculties:sense, imagination, memory and intellect, of whichonly the last can perceive truth, the other three play-ing subsidiary parts. What in us knows is purelyspiritual, not a bodily function nor conditioned by thebody. This power may cooperate with and apply itselfto sense, imagination and memory : it may attend tothem; but the activity of knowing is attributed to a sin-gle spiritual power only the vis cognoscens, by whichin the true sense, (proprie) we know. When its activ-ity is pure, then we are said intellegere, and thefaculty concerned is intelligence. It is in consequenceof this purely spiritual power alone that there is anyknowledge (properly so-called) in human experience.

Here, then, Descartes characterizes sense, imagin-ation and memory purely as the properties of bodilyfunctions and changes. It is only as such that there isanything distinctive about them. True, these bodilyfunctions and changes are connected with the activityof the spiritual faculty, which may attend to, and somake use of, them; but, strictly, sense, imagination2 Ibid., pp. 411-418.

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and memory are not different forms or grades ofknowing. The knowing is always the same through-out and is due to a single spiritual principle a com-mon, abstractly identical element in them all theactivity of the self-conscious or rational soul. Tocharacterize the three subsidiary faculties, therefore,we must attend to what is peculiar to them and leavethe intellect out.

So considered, in their proper nature, they are cor-poreal organs, with definite location and extension.The action of other parts of the body produces inthem, by the ordinary laws of extension and motion,physical changes : i.e. sensations, images, etc. 1 Descar-tes says, therefore, that we must regard sensation as achange in which we are passive. Our external partssensate, strictly, only by being acted upon. No doubt,when we apply our peripheral sense organs to anobject, it is an action which we initiate, but sensatingitself is a purely physical change in the organ. It is achange of shape or form (idea) produced by the objecton the surface of the organ, as real as the change ofshape on the surface of wax produced by a signet.This change of shape is instantaneously communicatedto the central part of the body, which Descartes (withthe Schoolmen) calls sensus communis, the CommonSense, but this communication involves no materialtransference. 2 In principle it is the same as the move-ment of the pen as it writes: that of the pen-pointbeing simultaneous with that of all parts of the penand of the pen as a whole.The peripheral organ of sense communicates to the

1 Cp. A. & T, X, pp. 412-13.2 Vide ibid., p. 414.

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central organ (sensus commums) changes ot shape orform (figura vel idea) and common sense stamps theseon the phantasia or imagination just as a signetstamps shapes in the wax (and this, be it noted, is nomere analogy but a literal comparison). The phantasiais a real part of the body (vera pars corporis), whichpossesses a determinate size and is situated in the brain.It can assume different shapes in its several portions,so that it can hold and retain a plurality of distinctshapes (or ideas). So regarded it is memory.The way in which the spiritual power (intellectus)cooperates with these bodily organs is not, according

to Descartes's account/ very clear. He says that eitherit receives a shape simultaneously from common senseand the imagination, or attends or applies itself toshapes preserved in the memory, or forms new shapesin the imagination. The vis cognoscens sometimes suf-fers and sometimes acts; is sometimes the signet andsometimes the wax, but here the simile is mereanalogy. There is nothing in physical things in theleast like the power of knowing.Hence the phantasia is a genuine part of the bodyand phantasmata are bodily changes in it. Descartesinsists that these alterations involve no material trans-ference from the external thing to the sense-organ(e.g. physical particles), or from the sense-organ to thesensus communis and from it to the phantasia. Clearlyhe wishes to free himself from the confused concep-tions of curious entities (like species intentionales) andthe use made of them by the theory of knowledgetaught at the Jesuit School of La Fleche in which he1 Ibid., pp. 415-16.


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had been brought up. 1 He is also anxious to emphasizethe contrast between the extended body and thepurely spiritual intelligence of mind. Yet he does stillretain material intermediaries between the mind whichknows and the object perceived : forms or shapes inimagination. And these phantasmata are genuinelycorporeal; yet they are somehow properties, or qualit-ies, not attached to any bodies or tied to any corporealsubstance. They are shapes or changes which travelwithout being attached to any material particles (cp.the modern notion of 'waves').This strange and obscure doctrine of the bodilyphantasia is always in the background of the Regulae.(ii) The Singleness of the vis cognoscens.Why does Descartes emphasize the singleness ofthe vis cognoscens? Is it in order to suggest themutual dependence of all truths and the unity of allsciences ? His language here and later suggests that thepower of knowing is single in an abstract (or monoto-nous) sense. All details in any region of the knowableand the different regions of knowledge are one merelyin the sense that they are all perceived by the one,single, undifferentiated power all bathed in thesingle, undifferentiated spiritual light. This seems toimply that the mutual interdependence of truths in ascience leaves the truths themselves unaffected. By a1 Cp. Gilson. La Philosophic de Saint Bonaventure, pp. 146 ff., onthe subject of phantasmata and the part they play in thetheories of Aquinas and the Schoolmen; esp. pp. 158 ff. onspecies intentionales in the Summa Philosophica of BrotherEustace of St. Paul, a textbook which Descartes himself studiedat school. In a letter written in 1640 (A & T, III, p. 185) hesays that he remembers some of it.24


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single science Descartes could mean an aggregate ofunit truths in mutual isolation, not a whole system oftruth. Similarly, if this is what he intends, the unityof the sciences seems only to mean that these collec-tions or complexes of unit truths may themselves begathered into an aggregate of aggregates. We do notyet, however, know properly how Descartes does un-derstand this singleness of the vis cognoscens or unityof the sciences.

RULES II AND IIIRULE ii : We ought to study exclusively subjectswhich our mind seems competent to know with a cer-tainty beyond all doubt.RULE in : In whatever subject we thus propose wemust enquire not what others believe but only whatcan be clearly perceived or with certainty inferred,these being the only ways in which genuine knowledgecan be acquired.

In the exposition of these two rules, there are twomain points to which we must attend : (i) Descartes'sattitude to Mathematics and (ii) his conception of thepower of knowing as comprising both intuitus anddeductio both insight and illation.The first will involve an account of Descartes's con-

ception of mathesis vera (or universalis) and thismay be postponed until we come to discuss Rule iv.But we may consider here why Descartes regardedmathematical science as the most perfect form ofscience, and what is its special propaedeutic power? 11 Cp. Discours, A. & T., VI, pp. 19-22.


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Two things impressed Descartes in the contemporary'vulgar' arithmetic and geometry : (i) its infallible cer-tainty and self-evidence 1 about any matter there isone truth only, so that a child who has done an addi-tion sum has found out all that the mind of man coulddiscover relative to it; (ii) the way in which this self-evidence expands to cover whole intricate problems.We frequently find a solution to a most complex prob-lem by long trains of reasoning in which each step isvery simple yet quite infallible, and the steps are soordered that we can go easily from one to another.Descartes was firmly convinced that knowledge, in theonly proper sense (scientia) is certain, evident, indubi-table and infallible in sharp contrast with conjectureand opinion, however probable, or thinking which issusceptible of doubt in however small degree.Nor must knowledge be confused with memory. Toremember is not, qua memory, the same thing as toknow; not even the memory of demonstrations. Wemight remember all Euclid without knowing it : forknowledge is spiritual insight into the matters whichmay be marshalled by memory.On this view no science (except, perhaps, arithmeticand geometry) will stand the test, and only mathemat-ics will survive this definition of knowledge. All othersciences give conclusions which are doubtful, or evenerrors; mathematics alone contains truth and nothingbut truth, free from falsity and doubt. How can thisbe ? Descartes early asked himself what gives absolutecertainty to this science : why the power of knowinghas only attained perfect realization here. And he con-cluded that it was due to the extreme purity and sim-1 Ibid., p. 21.


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plicity of the objects with which the geometer and thearithmetician are concerned. They presuppose nothingdependent on experience, nothing requiring confir-mation by experiment or observation. The data areentirely simple, abstract and precise; and these sciencesconsist in logical expansion of such data, rationallydeducing consequences from them.Now Descartes maintains that the power of know-ing is neither more nor less than (i) the power of seeingsimple data spiritual insight (intuitus) and (5i) thepower of moving uninterruptedly from simple to sim-ple the power of illation (illatio). This continuousmovement is such that all the links and every con-nexion are seen by the mind with the same immediateand infallible insight as that with which it intuits thedata themselves.

In arithmetic and geometry we have the only satis-factory realization of knowledge, precisely becausethey contain simple data such as it is the very nature ofthe intellect to perceive, and everything else is merelythe formation of chains in which simple is linked tosimple just such necessary expansion and connexionof data as it is the nature and function of the intellect,in its illative movement, to effect.So the essence of Descartes's method is (i) to admitno step which is not self-evident and (ii) in movingfrom step to step, to follow the inevitable logical order.This was the result of reflection upon the actual pro-cedure of geometry and arithmetic. He thought thatthese conditions would be fulfilled so long as the in-tellect worked according to its own proper nature. Buthe came immediately to the realization of defects inthe existing mathematical sciences and thought a new

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universal mathematics to be necessary. This broughthim to the conception of a possible universal and flaw-less mathematics. Tested by the two indispensablerequirements, even Arithmetic and Geometry, as thentaught, fell short of what he thought a perfect scienceought to be. This explains the guarded language at theend of the exposition of Rule ii : * that we should notstudy Geometry and Arithmetic alone, except fordisciplinary purposes (and even they would be betterserved by universal mathematics2). This rule then as-serts only that we must not study anything which isnot as certain as mathematics.Descartes's account of the Intellect(i) Intuitus. Descartes speaks at times as if intuitusand deductio were two quite distinct powers, faculties,or activities of the mind. It is, however, unlikely thathe ever held so crude a view, or, if he did, he soonabandoned it. Nevertheless, he begins by characteriz-ing intuitus as a distinct act or function of mind direc-ted upon a distinct and special kind of object. It isintellectual 'seeing' and has a certainty peculiar to it-self, which3 must not be confused with the vividnessof sense-perception or imagination.As an act of mind intuitus is a function of the intel-lect expressing its own nature. Sometimes what weintuit is a material or corporeal thing, or a relationbetween such things. In this case, imagination willhelp, if we visualize the bodies; or sensation may1 A. & T., x, p. 366.2 Vide Rule IV.3 Cp. Reg. III.

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help, if imagination is directed upon the shapes in thesensus communis. Still, intellectual seeing must beclearly distinguished from sensation and imagination,and its certainty must be clearly distinguished frommere imaginative (or sensational) assurance. So Descar-tes begins by explaining what he does not mean byintuitus.The intellectual certainty with which I see the mut-

ual implication of self-consciousness and existence isimmediate, like sense-perception; but, in the case ofsense-perception, my assurance fluctuates. Sensationflickers and varies according to the illumination, or thestate of my eyesight, or similar changing conditions.But the certainty of intellectual insight is steady, con-stant and absolute. To see a truth that x implies yis to see it absolutely and timelessly, once for all andunvaryingly.The danger of confusing intuitus with imaginatio

depends on the fact that, in both, two or more ele-ments are connected and the pictured union may bemore vivid than the conceived 'cohesion'. But wemust not confuse 'co-picturable' with 'co-thinkable'(conceivable) for these are not the same. Nor is 'un-picturable' the same as inconceivable.The text, however, is obscure. In Rule iii 1 he writes'Per intuitum intelligo non fluctuantem sensuum fid-em, vel male component's imaginationis judicium fal-lax' . And in Rule xii2 he seems to imply that idealelements may be composed in imagination in twoquite different ways: (i) as dictated by the intellectand (ii) alogically and arbitrarily, due to the order of1 A. & T., x, p. 368.2 Ibid., pp. 416 and 421-4.


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succession or co-existence originally produced in theperipheral organ of sense. This second kind of combin-ation may be accepted and confirmed by the subject,to whom it may dictate a judgement, which is thenlikely to be erroneous (male componentis imagination-is) for which imagination alone is responsible andwhich is apt to deceive us. Connexion resulting frommere casual association is doubtful, for, unless con-trolled by the intellect, imagination often connectsand compounds elements which do not really belongtogether and so should not be connected. Judging thisconnection to be fact, we are, consequently, in error.

Descartes's mature theory is that judgement involvesassent or dissent to a content conceived and thisassent or dissent is an act of will. This theory ishinted at in the last sentence of the exposition ofRule i; but apart from this hint he seems, at this stage,to be working without any special theory and to bemerely accepting the traditional scholastic view. InRule iii, belief is seen to be an obscure topic and iss^id to be an action, not of the mind but of the will. 1At this date, therefore, Descartes presumably did notattribute to the will judgements in which we assent torules we know or certainly apprehend. Likewise, inthe exposition of Rule xii,2 he distinguishes the facultyby which the intellect sees and knows (intuetur etcognoscit) from that which judges in affirming andnegating, and here the second faculty is not identifiedwith the will.Having shown what intuitus is not, Descartes goes

1 Ibid., p. 370 : ' . . . fides, quaecumque est de obscuris, noningenii actio sit, sed voluntatis.'

2 A. & T., X, p. 420.30


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on to state what it is. 1 It is a conception, formed bypure and attentive mind, so easy and distinct that nouncertainty remains. It is thus free from doubt, draw-ing its origin solely from the light of reason, and ismore certain, because more simple, than deductio,which, however, even in men, is (on certain condi-tions) infallible.

'Simplicity', here, does not mean that what isapprehended is atomic. Descartes speaks of 'simplenatures' (naturae simp/ices), but refers to them also aspropositions, and they are, in fact, always couplesof terms in immediate logical relation. Each is genuine-ly simple : the object is apprehended, not discursivelybut in its entirety; and both the object and the actitself are present together, all at once and withoutlapse. In the exposition of Rule iii 2 one of the charac-teristics by which intuitus is opposed to deductio ispraesens evidentia. This is essential to intuitus, but notto deductio, which can borrow its certainty from mem-ory. In the expositions of Rules xi and xii, the samepoint is brought out from the side of the object. In thefirst3 it is stated that a proposition must be apprehen-ded (i) clearly and distinctly and (ii) all at once, notsuccessively. And in the second4 we are told that wemust be in error if, in regard to a simple nature, wejudge that we know it in part only. It is either whollypresent and completely revealed or not at all; either itgives us the absolute and entire truth or no intellectualinsight at all.1 ibid., p. 368.1 Ibid., p. 370.

Ibid., p. 407.Ibid., p. 420.

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The origin of the whole doctrine is obviously Aris-totelian. Intuitus is the same as vowig, 'simple natures'are ra asrAa or ra a^tWera, and the truth ofintuitus is, like the truth of v6r}


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therefore, is a proposition in which two elements arein immediate but necessary connection as implicansand implication. A immediately and necessarily in-volves B an immediate necessary nexus of a couple ofelements. The nexus however need not be reciprocal,as Descartes specially tells us that it is not necessarythat B should immediately implicate A. 1 He thusspeaks of these self-evident data as propositiones orenunciationes* and he quotes, as further examples,'2 + 2= 4', '34-1=4', '2 + 2= 3+ i'.3 Yet he con-stantly speaks of these self-evident objects of intuitusin terms which suggest concepta an 'A' or a 'B' andnot a complex 'A implying B'. He speaks of them asres simplicissimae and naturae purae et simplices.

It is not easy, at first sight, to reconcile such passageswith what must be taken as his considered view : thatthe object is a nexus. There is a very puzzling passagein the exposition of Rule xii,4 which may be summar-ized as follows :We must distinguish what is a single thing, whenthings are considered per se, from what is single whenconsidered from the point of view (or as an object) ofour thought. E.g. a shaped body is a single thing whenconsidered 'ex parte rei', but as an object of our know-ledge it is complex it is compounded of three 'nat-urae' : body, extension and figure. Though thesehave never existed apart, they must be conceived sep-1 Ibid., p. 422.2 Ibid., pp. 369, 370; 379; 383.3 Ibid., p. 369.4 Ibid., pp. 418-425. Note : The doctrine is repeated in various

passages of Locke's Essay Concerning the Human Understand-ing. Locke lived in Holland from 1683 to 1689.

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arately before we can say that they are found togetherin one thing. In the Regulae we are concerned withthings qua objects of thought. Hence 'a single thing'must mean what is so clearly and distinctly conceivedthat we cannot divide it: e.g. duration, extension,figure, motion, etc.; i.e. it is a not further analysableobject of knowledge and thought. And it must be agenuine element of an object of knowledge, not a meregenerality or abstract universal. 1 For instance 'limit'(in 'Figure is the limit of extension'), is more generalthan 'figure' (for there may also be a limit of durationor motion), but it is not more simple. It is complex,being a conflation from many simple natures, com-pounded of several different ideas by disregardingtheir differences. It is applicable to all only equivoc-ally, and not applicable, in any definite sense, to any.

Descartes shows that all such simple objects ofthought fall into three classes: purely intellectual,purely material or corporeal, and those which arecommon to both. By the first he means objects ofthought which are intelligible to self-conscious beingsor spirits only, and which are known without anyimage or other corporeal aid (e.g. knowledge, ignor-ance, doubt, volition, and what these are). The secondare known to exist only in bodies, and intellectualinsight into them is facilitated by imagination or sen-suous presentation (e.g. figure, extension, motion). Thethird class of objects is common because they areattributable both to material bodies and to spiritsindifferently (e.g. existence, duration, unity). Wemust here include those common notions which arelinks connecting other simple natures and on the self-1 Cp. pp. 418-9.34


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evidence of which the conclusions of our demonstra-tions rest (e.g. identity, equality, etc.: two thingsequal to the same thing are equal to one another).These common objects may be known by inspection ofthe intellect, pure and alone, or so far as seeing imagesof material things reveals them to the intellect, Thelist of simple natures must be extended to include thecorresponding negations and privations of such con-cepts, so far as they are conceived by the mind : e.g.instant (the negation of duration), rest (the privationof motion), nothing (the negation of existence) and soon.

This and similar passages suggest a sharp distinctionbetween intuitus and deductio (common in phil-osophy), and the suggestion is confirmed in the nextparagraph, 1 where he distinguishes two faculties ofintellect, one which sees and knows, and one whichjudges by affirming and negating. There are certainsymbols which form, so to speak, the letters of thealphabet of reality universals pervading either allthings, spiritual and corporeal, or large areas of thereal, but, nevertheless, in some sense singular and sim-ple, They are fundamental constituents of all thatexists, and they themselves, though they do not (in thesame sense) exist, yet they subsist. They are in somesense there, confronting the mind, waiting for itsrecognition which is direct and immediate a simpleact of seeing. This is the only genuine knowledge, theonly real and absolutely certain grasp of truth, the in-dispensable precondition of judgement and reasoning,which by combining and arranging what we intuitgives a more precarious and derivative knowledge.1 Ibid., p. 420.

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Yet any such interpretation is not only in directconflict with what Descartes has said under the ear-lier Rules about simple propositions being the object ofintuitus, is not only in conflict with what he saysabout deductio, but can hardly stand and does not, oncloser examination, really emerge from the passageunder Rule xii, especially if we consider Descartes'sexamples and his manner of expressing himself.He says that no corporeal idea can be imagined suchas to represent to us what doubt, knowledge, etc.,really are. It seems, then, to be implied that what weintuitively perceive is 'that knowledge is so and so*.Again, speaking of the second class of simples, hesays that they are known to be only in bodies (thatduration is attributed to certain bodies, that 'this bodyis in motion', etc.); and, of the third, that they areattributed indifferently, now to spirits, now to cor-poreal things (e.g. 'that this mind exists', 'that thisbody is extended at rest, etc.'). There seems no roomfor hesitation if we bear in mind that Descartes adds tothe list of simple natures the principles of linkage ofour knowledge, the universally accepted laws ofthought. What the intellect perceives, then, is quiteclearly, at least two elements in one fact, two ele-ments in immediate and necessary cohesion. Thewhole fact, in necessary combination, implicans plusimplicandum is 'simple' in that it is a minimum ofknowledge. Nothing less is knowable at all. We can-not know 'A' nor 'B', nor 'implying' except in asingle unitary whole where all three are distinct (no

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doubt) but inseparable. If we know at all it must be'A implying B'.

(2) Deductio. The first mention of deductio is underRule vi, where it is contrasted with experience (empir-ical observation), and these (deductio and 'exper-ience') are regarded as two alternative ways by whichwe can arrive at a knowledge of things. Assuming thatwe begin with a self-evident truth, we may extend ourknowledge by rationally following the implicationsof the implicans the illation of one thing from an-other. Experience often misleads us, but deductio isquite as infallible as intuitus itself. We may fail tomake a deduction, we may fail to draw out what islogically implied, but no intellect at all rational canmis-infer or mis-think any more than it can mis-per-ceive. That is why mathematics is free from error; itis no more than the following out of the logical im-plications of simple, abstract and absolutely certaindata. These, if they are perceived at all, must be per-ceived as they are, and their implications, as logicallydrawn out, must be infallible. Observation, on theother hand is fallible.

So far deductio takes its place alongside intuitus asone of the two necessary and only acts of the viscognoscens. It is the very nature of the intellect toperform both of these activities, and thus we achieveknowledge without any deception. To understand isintellectually to perceive or to deduce or both, andintellectually to perceive or deduce is to understand.There is no such thing as false intuition or faultydeduction. So it appears that one of these native func-

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dons of the mind assures us of the data and the otherguarantees our advance from the data. 1

It cannot be denied that the interpretation heregiven is what Descartes intends. More than once in theRegulae he asserts the duality of original acts of theintellect and distinguishes intellectual vision from il-lative or discursive movement, and the perception ofsimple reals from the linkage or connexion betweensimple reals. But in spite of this explicit doctrine, thereruns through the Regulae a more adequate conceptionof the function of the intellect, though one incompati-ble with the doctrine expressed. This more adequatedoctrine, which first appears under Rule iii (just asDescartes is formulating the above, more crude,theory), is the more important for our present pur-pose.2 We need not discuss whether Descartes everwas a whole-hearted believer in the mechanicalanalysis of the power of knowing into two functionsand the corresponding division of the objects ofmind into simple natures and the linkages betweenthem. May he not simply have adopted an expositorydfevice ? If we think that he really believed it, we mustsuppose that he was later forced beyond it, but that henever became fully conscious of his own advance and1 In the passage under Rule III (A. & T., X, p. 368) : omnes

intellectus nostri actiones, per quas ad rerum cognitionemabsque ullo deceptionis metu possimus pervenire : admittuntur-que tantum duae, intuitus, scilicet et inductio' the word 'in-ductio' is probably an error in the MS., for under Rule IV(ibid., p. 372), Descartes refers again to this passage using theword 'deductio' (cp. also Reg. ix Exp., ibid., p. 400). The matter,however, is complicated by the fact that what Descartes meansby 'enumeratio sive inductio, is uncertain (cp. below, pp. 49-61).

2 Cp. p. 25 above.38


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so fell into verbal self-contradictions. On the assump-tion that he did not really hold such a view, we mustsuppose that his contradictions are corrections of whathe considers to be an inadequate way of expressing histheory.

Under Rule iii, Descartes proceeds to say : 'But thisself-evidence and certainty of intellectual insight isrequired not only for simple propositions but also forall discursive reasoning. For example, 2 and 2 yield thesame sum as 3 and i, in this case we must perceive notonly that 2 and 2 make 4, and 3 and i likewise make4, but also that the conclusion is a necessary conse-quence of these two propositions'. 1Under Rule xi we get the same idea: The simple

deduction of any one thing from another is effected bymeans of intellectual insight.2 And under Rule xii :'. . . the mind's insight extends to the apprehensionof simple propositions, their necessary linkages andeverything else which the intellect experiences withprecision'.3 Thus intuitus is needed for both linkagesand simple natures, and there is no sharp division be-tween the objects of intuitus and of deductio. Thedifficulty now is to distinguish deductio as an originalact or function of the intellect as a separate modeof knowledge at all. How is it 'other than' intuitus,as is alleged under Rule iii? 41 A. & T., X, p. 369. 2 Ibid., p. 407.3 Ibid., p. 425 : 'Atque perspicuum est, intuitum mentis, turn ad

Illas omnes extendi, turn ad necessarias iUarum inter se con-nexiones cognoscendas, turn denique ad relinqua omnia quaeintellectus practise, vel in se ipso, vel in phantasia esse ex-peritur'.

4 Ibid., pp. 369-70.39


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In order to bring out Descartes's better view we maybegin by giving the answer which he ought to havemade; then we shall outline the position to which heseems on the whole to have inclined (apart fromwaverings and contradictions), pointing out wherehe explicitly departs from it; and, thirdly, we shallattempt to confirm this interpretation by detailedreferences.

(a) Descartes ought to have said that two things arealways essentially involved in every act of knowing :

(i) a certain illative movement or discursus an in-tellectual analysis and synthesis in one which bringsto light distinguishable elements and at the same timepoints to the logical implication by which each leadsto the next the necessary connections by which theycohere; (ii) a certain unitary apprehension, an immed-iate, direct perception of the distinguishable elements(as opposed to isolable constituents) as indivisibly con-stituting a whole.Beyond this no further distinction of intuitus from

deductfo is possible or necessary. In principle bothmodes are essential and indispensable to any and everyact of knowing. And in principle the character of everycognoscibile and every cognitum must be such as toanswer to these two modes of apprehension. Nothingis or can be known unless it is unitary and whole andpresent before the mind in its wholeness, and unlesswithin this unity there are two or more distinguish-ables, so that it is discovered to the mind by a discur-sive movement at once analytic and synthetic. Thedistinguishables are seen in this discursus to be mut-ually implied, as it moves from one to the other alongthe line of logical connexion. The discursus is construc-


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of reality - knowable and known by the immediateintellectual apprehension of intuitus alone. These areat once elementary constituents of reality and thefoundations of all knowledge, (ii) At the other extremethere are certain remote consequences of these dataconnected to them by chains of reasoning effected byillative, discursive activity only. The apprehensionhere takes the form of construction (or re-construction)of the chain of reasoning, enabling us, not to see, butto infer the consequences from the primary data, (iii)Between these two there is an intermediate region ofknowledge, where what is known is both seen immed-iately (intuitively) and apprehended as demonstrable,or inferentially and necessarily deducible, from ulti-mate cognoscibilia.

Nevertheless, Descartes only maintains this com-promise with qualifications. First, some of his state-ments show that he waveringly recognizes that theapprehension of primary reals and truths involvesdiscursus and, secondly, the absence of immediate per-ception in long chains of reasoning is sometimesascribed to an infirmity in the human mind. 1 What hesays implies the recognition that so far as intuitus isabsent our knowledge is neither genuine nor perfect.

(c) Let us now consider what Descartes actually saysin more detail, (i) First, he states a kind of compromisedoctrine : some propositions may be said to be knownat times by intuitus, or at others by deductio, accord-ing to different points of view, but first principles areknown only by intuitus and remote conclusions onlyby deductio.

2It is only such as can be immediately

1 Cp. below on 'enumeratlo sive inductio', pp. 49ff.2 A. & T., X, p. 370.


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deduced from first principles to which the comprom-ise doctrine applies. Here the discursus may subserveperception, or perception assist the discursus. 1 Again,he says that many things, though not self-evident, mayyet be known with certainty, provided only that theyare deduced by a continuous and uninterrupted move-ment of thought from premises which are certain, andthat the thinker perceives clearly each single step.Though we cannot embrace all the links of the chainin one act of perception, we can apprehend the con-nexion of the last stage with the first, without, in thesame act, perceiving each several link, provided thatwe have seen all the links and their several connexionsand remember that each was necessarily connectedwith its neighbour. So deductio is contrasted withintuitus, first, as movement or succession, and secondlyso far as its certainty does not require the 'praesensevidentia' required by intuitus, but is in a mannerborrowed from the memory.2 The middle region ofany science or department of the knowable is, then,from different points of view, the object both ofintuitus and of deductio.

Yet Descartes maintains a sharp distinction betweendeductio and intuitus, even where they co-operate.Both may be indispensable for a genuine act of know-ledge, yet within that act each remains detachable;each remains what it was when it constituted imper-fect knowledge by itself. In fact each always remainsitself and what it is in isolation, even when both gotogether in one piece of knowledge. When Descartessays, or implies, that immediate apprehension and1 Cp. ibid., pp. 407-8.2 Ibid., p. 370.

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illation are inseparable and indispensable conditions ofany full act of knowledge, he still views them asconnected ab extra with each other. Each requires theother but is not fused with it. Thus, in order to knowthat 2 + 2 = 3+1 is a necessary consequence of thefact that 2 + 2 = 4 and 3+1=4, the intellect mustperceive by intuitus that 2 + 2= 4 an^ 3 + i=4> thenit must deduce the equality of 2 + 2 and 3 + 1, andfinally it must (again) perceive that the conclusion isa necessary consequence of the premises.

Descartes always tends to conceive reasoning as achain of links or sequence of states a movement ofthought along a chain of truths, each link being self-evident and the movement from link to link or ratherthe connexion of the second link to the first, after themovement has been made must be self-evident. Fromthis point of view, Descartes's deductio is the same asthe ideally perfect syllogism or owobttfyg of Aris-totle. It is true that he protests against syllogism,but unless he mistakes Aristotle he means by that thetraditional subsumptive syllogism of the Schoolmen.With that he will have nothing to do, nor with their'dialectical 1 reasoning. But his own deductio is, never-theless, the same as Aristotle's 'complete demonstra-tion 1 . For the perfect asro5g//, 'A must be Y', has toresolve the interval between A and Y into a successionof minimal, self-evident steps; 'A must be B; B must beC, etc., so that A will be seen to involve B, C, D, andso on, leaving nowhere any interval without imme-diate judgement. Thus, between A and Y a distancewill have to be traversed which, though completelyand exclusively covered by self-evident steps, is itselftoo great for the connexion between the remote ex-44


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tremes to be self-evident. This is the same as Des-cartes's doctrine.

(ii) Nevertheless, even the apprehension of a prim-ary truth or self-evident simple nature (as we havealready asserted) does involve discursus. This becomesapparent in Descartes's reply to the second set ofobjections to the Meditations. 1 The objectors urgeagainst Descartes that he asserts that nothing can beknown with absolute certainty unless and until the ex-istence of God the perfect, omnipotent and truthfulbeing is known; yet he claims in the second Medi-tation, though still as yet uncertain of God's existence,clear, distinct and indubitable knowledge of his ownexistence; and afterwards asserts that this must bededuced from the knowledge of God's existence. Des-cartes replies2 that 'cogito ergo sum' is a primaquaedam notio not deduced by syllogistic reasoning,yet at the same time he makes it clear that it is anexus in which two factors, implicans and implication,are necessarily involved. (He means by 'syllogismus',here, the bringing under a universal rule of a particularinstance 'syllogism' as understood by the School-men, but what Aristotle in the Posterior Analyticsrefuses to recognize as true syllogism and regards onlyas making explicit what is already implicitly known).Descartes easily shows that my own existence, so farfrom being deduced from a major premise, is prior toany universal major and I can only arrive at the certainknowledge of it by consciousness of what my ownexperience implies. Spinoza, in his summary of Descar-1 A. & T., vii, pp. 124-5.2 Ibid., p. 140.

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tes's philosophical principles/ follows this statementof Descartes's and rightly lays it down that 'cogitoergo sum' is not a syllogism; but when Spinoza goes onto summarise the position, saying that 'ego sum cogit-ans' is a single proposition equivalent to 'cogito ergosum', he has overshot the mark. For Descartes says2that a man learns the universal premise from the factthat he experiences in his own case the impossibilityof thinking unless he exists. This experience is said tobe a recognition by the simple insight of the mind,which seems very forcibly to emphasize that what themind intuites is a necessary nexus or implication.Thus 'cogito ergo sum' is, as Spinoza says, a single,unitary proposition (unica propositio). But Descarteshimself shows that it includes within itself an illationfrom one element to another. It is a mediate judge-ment, a concentrated or telescoped inference. The self-evident fact ('res per se nota') is 'that my thinkingnecessarily implies my existence'.We may compare this with what Descartes says inthe exposition of Rule xii.3 He has just been distingui-shing three classes of simple natures, all of which4(e.g. figure, extension, motion, and the like) areres per se notae. But he proceeds to say that they areconjoined or compounded with one another and thatthis conjunction is either necessary or contingent. It isnecessary when one is confusedly implied in the1 Renati des Cartes Trincipia Philosophiae, more geometricodemonstrate, I, Prolegomenon (Opera, Vol. IV, Van Vloten enLand, pp. 112-3).

2 Loc. cit.3 A. & T., X, p. 42i.4 vide, p. 420.

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lotion of the other so that we cannot conceive eitherproperly (if at all) if we try to conceive them as inde-pendent of each other: e.g. extension and figure ormotion and time. Likewise 4 + 3 = 7 is a necessarycomposition because the notion of seven must con-fusedly include those of four and three.The first part of this passage, in spite of its obviousformal inconsistency, must be treated with all respectbecause it contains the germ of an important latertheory of Descartes. The formal inconsistency is thathe says motion, extension, etc., are simple naturesper se notae out of which all our succeeding knowledgeis compounded; yet here motion, duration and figurehave become implicated in larger and more concreteconcepts, and it is these which are clear and distinct,per se notae, and knowledge of these is the necessaryprecondition to that of the so-called simple natures.This inconsistency, however, is of minor importanceWhat must be noted is that the line of thought hereimplied would lead to the recognition of two clearand distinct, or self-evident, natures only: substantiaextensa and substantia cogitans there would be anecessary system of extended implicantia and impli-cata and also one of spiritual implicantia and impli-cata. Here the Cartesian conception is adumbrated ofa physical universe, open to thought as a coherentsystem of mutually implicated data (motion exten-sion, figure, etc.), and its correlate, a corresponding,self-contained, coherent system of spiritual concepts.There is both external and internal logical coherence,and the physical universe is transparent to intellectualinsight because and in so far as thought distinguishescertain characters, and in recognizing them is driven

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to illate from one to another and see them as elementsof a self-integrating whole.But what are we to make of Descartes's statementabout 4 + 3= 7? We saw, in the explanation of Ruleiii, 1 that 2 + 2= 4 and 3 + 1=4 were cited as examplesof objects of intuitus, and intuitus alone. They werefacts which our intellect alone could directly see, noother method of cognition being required. We shouldexpect, therefore, that 3 + 4= 7 would be the same.But here it is called a composition of simple natures,and one which is necessary and not contingent be-cause the conception of 7 involves confusedly 3 and 4.What then are the 'simple natures'? 3 and 4, or 3+ 4, or 7 ? It seems that 3 and 4 could not be simple if7 is not. Yet the conception of 7 is clearly admitted toinclude the conceptions of 3 and 4 as well as their ad-dition. It seems that here Descartes, consciously ornot, does recognize a movement of thought withinand constituting the clear and distinct intellectualvision.

So far as any reasoning remains sheerly discursive,without there being any comprehensive conception,or immediate intuition covering the whole, suchreasoning is not itself knowledge but an imperfectsubstitute for knowledge a limitation or stunting ofknowledge which the mind accepts only because ofits infirmity. This also is implied at times by Descar-tes's express assertion, but to decide how far he inten-ded it we should have to be clear about the meaningof enumeratio sive inducio', which is very difficult todetermine and can be assigned only conjecturally.1 ibid., p. 369.48


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(3) Enumeratio sive inductio.Descartes holds that every possible subject of inquiry

is in principle intelligible that is, reality as a wholeand every department of the real, every one of itsparts, is a system of intelligibles necessarily connectedin inherent logical order. This logical order of linkagesis followed by the intellect in knowing, because and inso far as it is neither more nor less than the orderproper to intuitus and deductio. Intuitus reveals thefirst link in the chain, and provided we advance fromlink to link by correct logical illation, never breakingthe continuity, then every element of every part ofreality, as well as the whole, will, in due course bereached. In principle, then, careful logical analysis willenable us to find the links in any sphere of inquiry,so long as we adopt the proper logical order. Every-thing can be known in this way with the same certain-ty and by the same means. Nothing is too remote;everything can be reached with the same ease, and theknowledge of one thing is never more obscure thanthat of another, for all complexity consists in "rerumper se notarum compositio' (cp. Rule xii, Expos.).

Reality, as a whole is, accordingly, perfectly intel-ligible, and so is every group of facts; all are, and areknowable as, self-evident constituents self-evidentlyijiter-connected. That is so, at least in principle andideally i.e. it would be so for a mind which hadmastered every department of knowledge and expoun-ded or unfolded it all in the correct logical order as asingle chain of self-evident truths. Descartes, however,seems, at least from Rule v onwards, to conceive ideal-ly perfect knowledge as a network or system of chains,D 49


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rather than as a single chain; and, secondly, he regardseach link as less complex and more simple than itssuccessor more complex and less simple than itspredecessor. But no human mind is capable of master-ing every subject of inquiry and all knowledge, so thesum total of our knowledge could not unroll itself (infact) in a chain, or system of chains, self-evident inevery link.

If we reflect upon man's efforts to systematize hisknowledge, we shall notice the following three typicalcases : -

(i) A single line of logical implication lies straightahead of us, straight from what lies immediately beforeus to the conclusion or solution of our problem. In thismost favourable case, the whole problem the wholesegment of the real which is being studied has resolv-ed itself, bit by bit, into its ultimate self-evident con-stituents and their logically inevitable and self-evidentlinkages. The only difficulty here arises from thegrowing length of the chain. When we try to set outthe connexions in the best logical order to connectall the simples discovered, and arrange them as a con-tinuous inevitable illation, with every pair of simples,from first to last, self-evidently connected we some-times get a chain so long that we cannot keep it, all atonce and as a whole, within the grasp of our intellec^tual vision. We shall thus be forced to rely to someextent on our memory, and that is fallible. Strictlyspeaking we do not genuinely know the connexionof the last element with the first unless we can demon-strate it by an unbroken, continuous movement ofclear thought. This is never possible if any one link isso


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enumeration he goes on to describe 1 has no relevanceto the difficulty of the length of the chain (as opposedto the heterogeneity or complexity of the elements).It seems as if what he is advocating is no more thansome special rubrics for grouping the details thespecial proofs or parts of the chain in fact, any kindof mechanical device to help the memory.

(ii) But as a rule we are in a far less favourablesituation, for even if we are following a single line ofdirect logical implication from a simple datum, ourprogress may be barred by the nature of the facts(the obstinacy of nature) or by our own relative ignor-ance and inability. We are trying to resolve a particul-ar problem of a special science; but, in the first place,in defining and delimiting the several domains of thedifferent sciences, we do not divide reality into reallyseparate, self contained and independent worlds, so thedirect line of investigation may cut across the acceptedboundary marking off the domain of our specialscience from those of other sciences. The mathe-matician, for instance, proceeds along a chain ofmathematical reasoning, but he may find further pro-gress arrested by an inescapable barrier, if he comesupon a link which has no successor, or direct Implica-tum, within the domain of mathematics. The con-nexion would then, of necessity, be obscure to him asa mere mathematician, for the implicatum may belongto the domain of physics or optics. And, secondly,even if we could assume that the domain of eachscience is in fact self-contained and that the facts arelinked in a single chain, still we do not know thewhole science, but only work at a particular problem.1 A. & T., x, p. 388.


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Thus it would be very unlikely that the links we knowshould all be adjacent or neighbouring links in thechain, or that our analysis would unfold all the linksin all the parts. Consequently, we should from time totime come upon a link of which the immediate neces-sary implication is not obvious to us and will notbecome so until we have learned more.

(iii) But in many of our actual scientific reasoningsno single, direct line of implication exists, or themanner of our investigation tends to conceal it if itdoes. For we often move, not from simple to simple,but from many elements taken together to a simgleconsequent. The thread of implication is often twistedout of many strands. We must deduce our consequentfrom an antecedent in fact composed from a set ofco-ordinate links or elements each drawn from adifferent implicatory sequence. 1 We might have said'induce', rather than 'deduce', for this process isgenerally called 'induction'. In such cases advance isobstructed, not only by the growing length of thechain, but also by the complexity and heterogenietyof the data and the intricacy of their interconnection.Here, according to Descartes, enumeratio is essentialas an auxiliary of the deductive process. Indeed he isso impressed by its importance, that at times hespeaks of it as though it were an independent methodof proof and at others as if it were the only method ofproof, as opposed to direct intellectual insight.Now 'enumeratio sive inductio' is said to be illationor inference derived and composed from many dis-connected things (ex multis et disjunctis rebus collec-1 Cp. A. & T., X, p. 429, 11. 19-27.

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ta').1 In a passage describing the same logical proced-

ure, he speaks of 'proving by enumeration* and 'aconclusion drawn by induction'. 2 Yet in at least twoother passages he treats of 'enumeratio* as the onlyform of deductio genuinely distinct from 3 and in noway reducible to intuitus* Here Descartes says : Thisis an opportunity to explain more clearly what wasearlier said about intellectual insight: since in oneplace we contrasted it with deduction and in anotherwith enumeration only ...' (i.e. not with deduction ingeneral but with enumeration in particular). Simplededuction of one thing from another takes placethrough intuition (per intuitum), and for this twoconditions must be satisfied : The proposition must beapprehended (a) clearly and distinctly, and (b) alltogether, not part by part. But, a deduction, whenconsidered as about to be made, does not seem to takeplace all together. According to the exposition of Ruleiii, deductio is a movement of the mind, inferring onething from another. So deductio is rightly distinguish-ed from and contrasted with intuitus. But, if weconsider a deduction as already made, it is not amovement but the termination of a movement ('nullum motum . . . sed terminum motus'*). Therefore,when the content deduced is simple and manifest, wesuppose it to be seen by intuitus. When it is complexand involved, we take a different view, and give theprocess the name 'enumeratio' or 'inductio', because1 Reg. xi, A. & T., X, p. 407. Cp. Reg. vii, p. 389.2 Ibid., p. 390.3 Ibid., p. 389.* Ibid., pp. 407-8.5 Ibid., p. 408.

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the conclusion cannot be apprehended as a whole, andits certainty depends in part upon memory (i.e. itdepends on judgements specified in many and variousparts of the proof).Yet, after all, if these passages only are considered,Descartes has shown no more than that, in complicat-ed processes of reasoning, enumeratio sive inductio isa useful, indeed an indispensable, aid to proof. Induc-tion is useful where the chain of reasoning is long, andin complex arguments where we have to lean moreupon memory because the steps are too heterogenousto be perceived as a whole. A methodical grouping ofthese data and the numbering of the steps of the com-pleted argument are necessary to prevent them fromslipping from the memory or becoming disarranged. Sofar, then, enumeratio is not a mode of proof at all. Itsfunction is to arrange and group premises alreadyintuited and steps of an argument already deduced, inorder to help retention in the memory. It is not amethod by which to acquire fresh premises or to inferanything fresh from premises we already have.

But some other passages in the Regulae modify thisposition. In the exposition of Rule vii he says that thisenumeration, or induction, is a scrutiny (perquisitioa Baconian term) of everything relevant to the prob-lem before us, careful and accurate enough for us toknow that we have left out nothing of importancewhich ought to have been included; so that even if wefail to solve our problem we have advanced ourknowledge at least to the extent that we perceive thatthe object for which we sought could not have beendiscovered by any method known to us. If we have

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surveyed all methods open to man, we may say thatsuch knowledge is beyond the human mind.This explains why Descartes often uses enumeratio

as a preliminary survey of the ground before he at-tempts to solve a problem. For instance in the exposi-tions of Rules viii and xii - we are given a survey of theimplications of knowledge in regard to both possibleobjects of knowledge and possible instruments orpowers of knowing. Both these passages are prelimin-ary to an attempt to show the limits and range of thehuman intellect. Similarly in the exposition of Rulevii2 the example is given of surveys preliminary to theproofs that the area of a circle is greater than that ofany other figure of equal periphery, and that therational soul is not corporeal.

Again in the Treatise on Dioptrics,3 Descartes isabout to explain the means of perfecting humanvision : to determine what kinds, shapes and arrange-ments of lenses are most suitable for new opticalinstruments. He begins by saying that he wishes tomake an enumeration of the improvements which artcan supply, after enumerating the natural provisions :(i) bodies, the objects of vision; (ii) the interior organsreceiving the action of these bodies, and (iii) theexterior organs, the eye and the media of vision,which dispose these objects so that their action canbe properly received by the inner organs. ^

Descartes, then, considers these three heads one byone and makes the relevant distinctions; he discussespossible hindrances and aids, setting aside those which1 Ibid., pp. 395-6 and pp. 411-25.2 p. 390.8 A. & T., VI, pp. 147!


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are clearly impossible and estimating what obstablesand deficiencies cannot be removed by human know-ledge.

These enumerations are clearly a preparatory map-ping of the whole province of study, in some cornersof which special investigation is to take place, and thesolution of special problems to be found. The enumer-ation ensures that we see and consider whatever, inthe province of the science as a whole, may berelevant to the special inquiry. In the wider domainthere may be links essential to chains of reasoningrequired to solve the special problem (or problems).We must not disregard any link, or our subsequentconclusion may be invalidated.

But it is not easy to see how, on Descartes's theory,it is possible to make a preliminary survey at all.In the conduct of such surveys he does not say whatour power of knowing is. A logical procedure isimplied for which he does not seem to have allowedin his account of the intellect, as exhausted by intuitusand deductio. For preparatory surveys of this sort areof necessity general and abstract, and Descartes saysthey must be 'sufficient' that is, to guard against theomission of anything which will be relevant to theproblem subsequently investigated. 1 Further, theymust be ordered that is, conducted upon some prin-ciple indeed any principle would do, provided it gavea comprehensive, convenient and time-saving arrange-ment. The enumerations are, therefore, always tosome extent, and usually in the main, skeleton out-lines; in fact, a sufficient enumeration need be littlemore than a disjunctive limitation of the gaps in our1 Cp. A. & T. X, pp. 589-90.


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Enumeratio is not, therefore, a method of proof atall. Descartes gives the name to two distinct devices:one for retaining in the memory the data from whichinference has already been made; and the other a pre-liminary survey of the ground to select, compare andarrange the materials for an inference which is aboutto be made. The inference itself is always a movementof illation from one simple to another by the intellect

deductio. This passage (or transition) constitutes alinkage (or implication) which is self-evident, as arethe inter-linked simples themselves. The linkage, infact, is in principle identical with the nexus betweenimplicans and implication within each single self-evident proposition.

Against this interpretation it may be said that Des-cartes frequently speaks of inductio, and, in one pas-sage, of imitatio, suggesting that these are modes ofproof other than deductio or intuitus. But he expresslyidentifies the power of knowing with deductio andintuitus alone. 1 Also he identifies inductio with special-ly intricate form of deductio, where the premises arecomplex or confused; and he gives no explanation ofimitatio in connexion with inductio.The one passage in which imitatio is mentioned

2

is very difficult, and since it has a bearing uponDescartes's method, we have good reason to examine'it.

In actual inquiries we may sometimes come upon alink the implications of which, and therefore its im-mediate logical successor in the chain, are obscure,and advance is accordingly barred. There are two1 Reg. xii, p. 425, 11. 10-12.2 Cp. Reg. viii, pp. 393-5-

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possible varieties of such situations: (i) The barriermay be absolute and insuperable owing to the limita-tion of the human mind. 1 (ii) The barrier may be in-superable only for those who confine themselves with-in the limits of a special science, but may be sur-mounted by those who pursue the universal aim ofscience and follow the principle of the Cartesianmethod. As stated under Rule I, the student's interestought not to be confined to a single science, but heought to study all. Descartes gives as an example thefollowing problem:

Suppose a student whose interest is confined to puremathematics sets out to discover the line of refractionin optics. Such a student will follow the method ofanalysis and synthesis, set out in Rules v and vi, andwill see that the determination of this line dependsupon the relation between the angles of incidence andthd angles of refraction.2 He will recognize that thediscovery of this requires a knowledge of physics andis impossible for the pure mathematician, so he willbreak off his inquiry.But now suppose a student whose aim is universal :he will desire to pass a true judgement here also,and, as a genuine student of all the sciences, he will beable to complete the analysis, proceeding until hereaches the simplest link in the implicatory sequenceinvolved in the problem. He will find that the ratiovaries in accordance with the variation in the anglesresulting from changes in the physical media, and thatthese again are dependent upon the mode of propaga-1 Vide Reg. v'm, p. 396. No example is given though he says thatmany such cases may occur.

2 Cp. La Dioptrique A. & T. VI, pp. 100-1, 211-214.60


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tion of the rays of light. He will find that knowledgeof this propagation requires a knowledge of the natureof illumination; and that again presupposes the know-ledge of what a natural force, or energy, is. In thelast presupposition the student has reached the simp-lest link in the implicatory sequence (for this problem),and, having gained a clear insight, he will now (inaccordance with Rule v) begin his synthesis link bylink.

If now he finds himself unable to perceive thenature of illumination, he will enumerate all the otherforms of natural force (in accordance with Rule vii),so that he may understand, at least by the analogy'imitatio') of what he knows of the other naturalforces. Descartes promises a later explanation of imi't-atio, but this promise remains unfulfilled, probablybecause the Regulae was never completed. He seemsto have in mind a process of hypothetical construction,in this instance, of the nature of illumination byanalogy from the nature of some other natural forcewhich is known to the inquirer and which it may besupposed to resemble. 11 Cf. Reg. xiv, A. & T. X, pp. 438-9.

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subject matter is treated) does little more than workout in detail what they cover in general. In the dis-cussion of enumeratio we have already dealt withRule vii, so we may now consider the exposition ofRule iv 1 and Rules v and vi.2

Descartes says that nearly all chemists, most geomet-ers and the majority of philosophers pursue theirstudies haphazard without any method at all. Occasion-ally these aimless studies lead accidentally to truth,but these coincidental cases are more than outweighedby the serious injury done by such procedure to themind, because vague and confused studies weaken thenatural light. That is why people with little or nolearning are often far superior in forming clear andsound judgements on the ordinary matters of life.By a method he means certain and easy rules such

that anyone who precisely obeys them will nevertake for truth anything that is false, and will advancestep by step, in the correct order without waste ofmental energy, to the knowledge of everything thathe is capable of knowing. But he suggests that it is notthe method which enables us to know, for it is thenature of the intellect to perceive what is clear anddistinct and also to move infallibly from one self-evident link to the next, along the line of logicalimplication. Not only are intuitus and deductio the"Sole means of knowing this they must be in order tobe vis cognoscens at all but we could not learn touse them, because we should have to use them inorder to learn, and unless we both possess and use themfrom the first we could get nowhere. But, says Descar-1 pp. 371-2.2 pp. 379-87-

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tes, if we use the method, we can increase, guide andexercise the powers of intuitus and deductio. We canso arrange the materials, on which our power ofintellectual vision is to be turned, and the links whichare to form the stages of illation, that our naturalpowers will work under the most favourable condi-tions and will develop in scope and in intensity.The general principles of the method are set out inRules v, vi and vii and the details in Rules ix, x andxi: Those applying to intuitus come under Rule ix,those concerning deductio, in more complex cases,under Rule x, and those applying to cases where bothtogether and concomitantly are to be used, under Rulexi.The entire method consists in the ordering and

arrangement of material on which attention is to beConcentrated. Exact observance of it will be secured ifwe reduce involved and complex propositions to sim-ple ones and begin by exercising our intellect (in-tuitus) 1 on the simple, and then work our way up stepby step to all the others. In the exposition of thisRule,2 Descartes emphasises its supreme importance.Here as elsewhere, he warns us against the neglect ofthe simple and easy. Many

descartes s rules for the direction of the mind 1957

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